What is the sum of all the three-digit positive integers?
Solution: We want to evaluate the arithmetic series $100 + 101 + \cdots + 999$.   The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms.  The total number of three-digit integers is $999 - 100 + 1 = 900$, so the sum is $(100 + 999)/2 \cdot 900 = \boxed{494550}$.